Boolean Modifier acts like the object has no volume
I noticed the scale of the two objects are different so I'm assuming you scaled one of them.

If you resized the cube or cylinder try using 'apply object transform' and mark the scale and rotation. Probably even if you see the object as smaller or bigger, Blender doesn't take into account that the object has a new volume.

Most of the times it will fix things so that afterwards you can successfully apply the Boolean modifier.